% The function sc_init_cond.m computes the initial values of the
% systemic circulation. The initial values are computed based
% on conservation laws of a linearized model.
%
% Function arguments:
% th - vector containing the initial parameter values
%
% Function outputs:
% P - a 6x1 vector containing the six initial pressures
% = [Pl(0); Pa(0); Pv(0); Pr(0); Ppa(0); Ppv(0)]
% Q - a 6x1 vector containing the six initial volumes
% = [Ql(0); Qa(0); Qv(0); Qr(0); Qpa(0); Qpv(0)]
% q - a 6x1 vector containing the six initial flow rates
% = [qpv(0); ql(0); qa(0); qv(0); qr(0); qpa(0)]
% ve - a 2x1 vector containing the initial variable elastance values
% = [El(0); Er(0)];
%
function [P,Q,q,ve] = sc_init_cond(th)
% Storing nonlinear ventricular compliance values for
% subsequent initial ventricular volume calculation.
Cld = th(2);
Crd = th(6);
% Converting ventricular compliances to linear values which
% is necessary for estimating initial pressures.
th(1) = th(1)*((th(26)-th(9))/th(31));
th(2) = th(2)*((th(26)-th(9))/th(31));
th(5) = th(5)*((th(27)-th(12))/th(32));
th(6) = th(6)*((th(27)-th(12))/th(32));
% Estimating initial pressures.
Ts = .3*sqrt(1/th(22));
Td = 1/th(22) - Ts;
temp = -th(6)*th(23) + th(5)*th(23);
b = [temp+(Ts*th(28)/th(18));
temp;
temp;
th(33)*(th(3)+th(4))];
A = [0, 0, (Ts/th(18))+th(5), -th(6);
0, Td/th(17), th(5), (-(Td/th(17))-th(6));
1/(th(22)*th(16)), -1/(th(22)*th(16)), th(5), -th(6);
th(3), th(4), 0, 0];
x = A\b;
P = [th(33) x(1) x(2) x(4) th(33) th(33)]';
% Establishing initial flow rates.
q = zeros(6,1);
if (P(6) > P(1))
q(1) = (P(6)-P(1))/th(20);
else
q(1) = 0;
end
if (P(1) > th(33))
q(2) = (P(1)-th(33))/th(15);
else
q(2) = 0;
end
q(3) = (P(2)-P(3))/th(16);
if (P(3) > P(4))
q(4) = (P(3)-P(4))/th(17);
else
q(4) = 0;
end
if (P(4) > th(28))
q(5) = (P(4)-th(28))/th(18);
else
q(5) = 0;
end
q(6) = (P(5)-P(6))/th(19);
% Establishing initial variable ventricular elastance values.
ve = [1/th(2) 1/th(6)]';
% Establishing initial volumes.
Q = [th(2) th(3) th(4) th(6) th(7) th(8)]'.*(P-th(23)*[1 0 0 1 1 1]') + [th(9:14)];
if (P(1) <= th(23))
Q(1) = th(9)*(2/pi)*atan(((P(1)-th(23))/((2/pi)*th(9)*ve(1)))) + th(9);
else
yl = (P(1)-th(23))/th(31);
xl = vent_vol(0.5,yl,1/Cld);
Q(1) = (th(26)-th(9))*xl+th(9);
end
if (P(4) < th(23))
Q(4) = th(12)*(2/pi)*atan(((P(4)-th(23))/((2/pi)*th(12)*ve(2)))) + th(12);
else
yr = (P(4)-th(23))/th(32);
xr = vent_vol(0.5,yr,1/Crd);
Q(4) = (th(27)-th(12))*xr+th(12);
end